Biomedical networks are universal descriptors of systems of interacting elements, from protein interactions to disease networks, all the way to healthcare systems and scientific knowledge. Long-standing principles of network biology and medicine, while often unspoken in machine learning research, can provide the conceptual grounding for deep graph representation learning, explain its current successes and limitations, and inform future advances (Li et al. 2021). In this talk, I first synthesize a spectrum of algorithmic approaches that, at their core, leverage topological features to embed networks into compact vector spaces. I then highlight how deep graph representation learning techniques have become essential for studying molecules, genomics, therapeutics, and entire healthcare systems. I conclude with two vignettes where we develop graph neural networks for predicting disease outcomes (Alsentzer et al. 2020) and disentangling single cell behaviors.